LMFDB - Embedded newform 136.3.t.a.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			65.2
Character	$\chi$	$=$	136.65
Dual form			136.3.t.a.113.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.533765 + 2.68342i) q^{3} +(-4.10611 + 2.74362i) q^{5} +(-5.75863 - 3.84780i) q^{7} +(1.39909 + 0.579524i) q^{9} +O(q^{10})$	\(q+(-0.533765 + 2.68342i) q^{3} +(-4.10611 + 2.74362i) q^{5} +(-5.75863 - 3.84780i) q^{7} +(1.39909 + 0.579524i) q^{9} +(-14.2338 + 2.83128i) q^{11} +(-8.40728 - 8.40728i) q^{13} +(-5.17057 - 12.4829i) q^{15} +(15.9413 + 5.90538i) q^{17} +(-19.3881 + 8.03080i) q^{19} +(13.3990 - 13.3990i) q^{21} +(4.46220 + 22.4330i) q^{23} +(-0.234360 + 0.565794i) q^{25} +(-15.9822 + 23.9190i) q^{27} +(-4.08770 - 6.11768i) q^{29} +(12.6698 + 2.52018i) q^{31} -39.7065i q^{33} +34.2025 q^{35} +(-2.00841 + 10.0970i) q^{37} +(27.0478 - 18.0727i) q^{39} +(60.2557 + 40.2616i) q^{41} +(27.8507 + 11.5362i) q^{43} +(-7.33483 + 1.45899i) q^{45} +(-40.3775 - 40.3775i) q^{47} +(-0.395167 - 0.954017i) q^{49} +(-24.3555 + 39.6252i) q^{51} +(54.7887 - 22.6942i) q^{53} +(50.6777 - 50.6777i) q^{55} +(-11.2013 - 56.3128i) q^{57} +(-2.81393 + 6.79342i) q^{59} +(-45.0615 + 67.4393i) q^{61} +(-5.82698 - 8.72069i) q^{63} +(57.5876 + 11.4549i) q^{65} -58.3669i q^{67} -62.5788 q^{69} +(2.20576 - 11.0891i) q^{71} +(-60.7769 + 40.6098i) q^{73} +(-1.39317 - 0.930886i) q^{75} +(92.8615 + 38.4645i) q^{77} +(-95.7936 + 19.0545i) q^{79} +(-46.0167 - 46.0167i) q^{81} +(31.0115 + 74.8684i) q^{83} +(-81.6590 + 19.4888i) q^{85} +(18.5982 - 7.70361i) q^{87} +(-117.689 + 117.689i) q^{89} +(16.0649 + 80.7640i) q^{91} +(-13.5254 + 32.6532i) q^{93} +(57.5761 - 86.1688i) q^{95} +(-69.3086 - 103.728i) q^{97} +(-21.5552 - 4.28760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.533765	+	2.68342i	−0.177922	+	0.894472i	0.783919	+	0.620863i	$0.213218\pi$
$3$	−0.533765	+	2.68342i	−0.177922	+	0.894472i	−0.961841	+	0.273610i	$0.911782\pi$
$4$		0			0
$5$	−4.10611	+	2.74362i	−0.821222	+	0.548723i	−0.893710	−	0.448646i	$-0.851906\pi$
$5$	−4.10611	+	2.74362i	−0.821222	+	0.548723i	0.0724871	+	0.997369i	$0.476906\pi$
$6$		0			0
$7$	−5.75863	−	3.84780i	−0.822662	−	0.549685i	0.0714940	−	0.997441i	$-0.477223\pi$
$7$	−5.75863	−	3.84780i	−0.822662	−	0.549685i	−0.894156	+	0.447756i	$0.852223\pi$
$8$		0			0
$9$	1.39909	+	0.579524i	0.155455	+	0.0643915i
$10$		0			0
$11$	−14.2338	+	2.83128i	−1.29398	+	0.257389i	−0.793613	−	0.608423i	$-0.791803\pi$
$11$	−14.2338	+	2.83128i	−1.29398	+	0.257389i	−0.500370	+	0.865812i	$0.666803\pi$
$12$		0			0
$13$	−8.40728	−	8.40728i	−0.646714	−	0.646714i	0.305483	−	0.952197i	$-0.401182\pi$
$13$	−8.40728	−	8.40728i	−0.646714	−	0.646714i	−0.952197	+	0.305483i	$0.901182\pi$
$14$		0			0
$15$	−5.17057	−	12.4829i	−0.344705	−	0.832191i
$16$		0			0
$17$	15.9413	+	5.90538i	0.937726	+	0.347375i
$17$	15.9413	+	5.90538i	0.937726	+	0.347375i
$18$		0			0
$19$	−19.3881	+	8.03080i	−1.02042	+	0.422674i	−0.829247	−	0.558882i	$-0.811231\pi$
$19$	−19.3881	+	8.03080i	−1.02042	+	0.422674i	−0.191177	+	0.981556i	$0.561231\pi$
$20$		0			0
$21$	13.3990	−	13.3990i	0.638047	−	0.638047i
$22$		0			0
$23$	4.46220	+	22.4330i	0.194009	+	0.975348i	0.947953	+	0.318410i	$0.103149\pi$
$23$	4.46220	+	22.4330i	0.194009	+	0.975348i	−0.753945	+	0.656938i	$0.771851\pi$
$24$		0			0
$25$	−0.234360	+	0.565794i	−0.00937438	+	0.0226318i
$26$		0			0
$27$	−15.9822	+	23.9190i	−0.591933	+	0.885890i
$28$		0			0
$29$	−4.08770	−	6.11768i	−0.140955	−	0.210954i	0.754275	−	0.656559i	$-0.227989\pi$
$29$	−4.08770	−	6.11768i	−0.140955	−	0.210954i	−0.895230	+	0.445605i	$0.852989\pi$
$30$		0			0
$31$	12.6698	+	2.52018i	0.408703	+	0.0812961i	0.395160	−	0.918612i	$-0.370689\pi$
$31$	12.6698	+	2.52018i	0.408703	+	0.0812961i	0.0135429	+	0.999908i	$0.495689\pi$
$32$		0			0
$33$		−	39.7065i		−	1.20323i
$34$		0			0
$35$	34.2025			0.977213
$36$		0			0
$37$	−2.00841	+	10.0970i	−0.0542813	+	0.272891i	−0.998389	−	0.0567478i	$-0.981927\pi$
$37$	−2.00841	+	10.0970i	−0.0542813	+	0.272891i	0.944107	+	0.329639i	$0.106927\pi$
$38$		0			0
$39$	27.0478	−	18.0727i	0.693532	−	0.463403i
$40$		0			0
$41$	60.2557	+	40.2616i	1.46965	+	0.981990i	0.994792	+	0.101928i	$0.0325011\pi$
$41$	60.2557	+	40.2616i	1.46965	+	0.981990i	0.474860	+	0.880062i	$0.342499\pi$
$42$		0			0
$43$	27.8507	+	11.5362i	0.647692	+	0.268283i	0.682249	−	0.731120i	$-0.261002\pi$
$43$	27.8507	+	11.5362i	0.647692	+	0.268283i	−0.0345572	+	0.999403i	$0.511002\pi$
$44$		0			0
$45$	−7.33483	+	1.45899i	−0.162996	+	0.0324219i
$46$		0			0
$47$	−40.3775	−	40.3775i	−0.859095	−	0.859095i	0.132136	−	0.991232i	$-0.457816\pi$
$47$	−40.3775	−	40.3775i	−0.859095	−	0.859095i	−0.991232	+	0.132136i	$0.957816\pi$
$48$		0			0
$49$	−0.395167	−	0.954017i	−0.00806463	−	0.0194697i
$50$		0			0
$51$	−24.3555	+	39.6252i	−0.477559	+	0.776965i
$52$		0			0
$53$	54.7887	−	22.6942i	1.03375	−	0.428193i	0.199685	−	0.979860i	$-0.436008\pi$
$53$	54.7887	−	22.6942i	1.03375	−	0.428193i	0.834064	+	0.551668i	$0.186008\pi$
$54$		0			0
$55$	50.6777	−	50.6777i	0.921413	−	0.921413i
$56$		0			0
$57$	−11.2013	−	56.3128i	−0.196514	−	0.987944i
$58$		0			0
$59$	−2.81393	+	6.79342i	−0.0476937	+	0.115143i	−0.945931	−	0.324368i	$-0.894848\pi$
$59$	−2.81393	+	6.79342i	−0.0476937	+	0.115143i	0.898237	+	0.439511i	$0.144848\pi$
$60$		0			0
$61$	−45.0615	+	67.4393i	−0.738713	+	1.10556i	0.251751	+	0.967792i	$0.418994\pi$
$61$	−45.0615	+	67.4393i	−0.738713	+	1.10556i	−0.990464	+	0.137770i	$0.956006\pi$
$62$		0			0
$63$	−5.82698	−	8.72069i	−0.0924917	−	0.138424i
$64$		0			0
$65$	57.5876	+	11.4549i	0.885963	+	0.176229i
$66$		0			0
$67$		−	58.3669i		−	0.871147i	−0.900153	−	0.435574i	$-0.856546\pi$
$67$		−	58.3669i		−	0.871147i	0.900153	−	0.435574i	$-0.143454\pi$
$68$		0			0
$69$	−62.5788			−0.906940
$70$		0			0
$71$	2.20576	−	11.0891i	0.0310670	−	0.156185i	−0.962138	−	0.272563i	$-0.912129\pi$
$71$	2.20576	−	11.0891i	0.0310670	−	0.156185i	0.993205	+	0.116379i	$0.0371286\pi$
$72$		0			0
$73$	−60.7769	+	40.6098i	−0.832560	+	0.556299i	−0.897207	−	0.441609i	$-0.854408\pi$
$73$	−60.7769	+	40.6098i	−0.832560	+	0.556299i	0.0646475	+	0.997908i	$0.479408\pi$
$74$		0			0
$75$	−1.39317	−	0.930886i	−0.0185756	−	0.0124118i
$76$		0			0
$77$	92.8615	+	38.4645i	1.20599	+	0.499539i
$78$		0			0
$79$	−95.7936	+	19.0545i	−1.21258	+	0.241196i	−0.759639	−	0.650345i	$-0.774624\pi$
$79$	−95.7936	+	19.0545i	−1.21258	+	0.241196i	−0.452938	+	0.891542i	$0.649624\pi$
$80$		0			0
$81$	−46.0167	−	46.0167i	−0.568107	−	0.568107i
$82$		0			0
$83$	31.0115	+	74.8684i	0.373633	+	0.902029i	0.993128	+	0.117029i	$0.0373371\pi$
$83$	31.0115	+	74.8684i	0.373633	+	0.902029i	−0.619496	+	0.785000i	$0.712663\pi$
$84$		0			0
$85$	−81.6590	+	19.4888i	−0.960695	+	0.229280i
$86$		0			0
$87$	18.5982	−	7.70361i	0.213772	−	0.0885472i
$88$		0			0
$89$	−117.689	+	117.689i	−1.32235	+	1.32235i	−0.410482	+	0.911869i	$0.634640\pi$
$89$	−117.689	+	117.689i	−1.32235	+	1.32235i	−0.911869	+	0.410482i	$0.865360\pi$
$90$		0			0
$91$	16.0649	+	80.7640i	0.176538	+	0.887516i
$92$		0			0
$93$	−13.5254	+	32.6532i	−0.145434	+	0.351109i
$94$		0			0
$95$	57.5761	−	86.1688i	0.606065	−	0.907040i
$96$		0			0
$97$	−69.3086	−	103.728i	−0.714522	−	1.06936i	−0.994019	−	0.109210i	$-0.965168\pi$
$97$	−69.3086	−	103.728i	−0.714522	−	1.06936i	0.279497	−	0.960147i	$-0.409832\pi$
$98$		0			0
$99$	−21.5552	−	4.28760i	−0.217730	−	0.0433091i
$100$		0			0
$101$		−	82.7991i		−	0.819793i	−0.912132	−	0.409896i	$-0.865565\pi$
$101$		−	82.7991i		−	0.819793i	0.912132	−	0.409896i	$-0.134435\pi$
$102$		0			0
$103$	160.258			1.55590			0.777950	−	0.628326i	$-0.216260\pi$
$103$	160.258			1.55590			0.777950	+	0.628326i	$0.216260\pi$
$104$		0			0
$105$	−18.2561	+	91.7795i	−0.173867	+	0.874090i
$106$		0			0
$107$	59.2751	−	39.6063i	0.553973	−	0.370153i	−0.246851	−	0.969054i	$-0.579396\pi$
$107$	59.2751	−	39.6063i	0.553973	−	0.370153i	0.800823	+	0.598901i	$0.204396\pi$
$108$		0			0
$109$	−81.7857	−	54.6475i	−0.750328	−	0.501353i	0.120638	−	0.992697i	$-0.461506\pi$
$109$	−81.7857	−	54.6475i	−0.750328	−	0.501353i	−0.870966	+	0.491344i	$0.836506\pi$
$110$		0			0
$111$	−26.0223	−	10.7788i	−0.234435	−	0.0971063i
$112$		0			0
$113$	−142.644	+	28.3737i	−1.26234	+	0.251094i	−0.780494	−	0.625163i	$-0.785032\pi$
$113$	−142.644	+	28.3737i	−1.26234	+	0.251094i	−0.481843	+	0.876258i	$0.660032\pi$
$114$		0			0
$115$	−79.8698	−	79.8698i	−0.694520	−	0.694520i
$116$		0			0
$117$	−6.89036	−	16.6348i	−0.0588919	−	0.142178i
$118$		0			0
$119$	−69.0777	−	95.3459i	−0.580485	−	0.801226i
$120$		0			0
$121$	82.7959	−	34.2952i	0.684264	−	0.283431i
$122$		0			0
$123$	−140.201	+	140.201i	−1.13985	+	1.13985i
$124$		0			0
$125$	−24.6758	−	124.053i	−0.197406	−	0.992428i
$126$		0			0
$127$	11.3601	−	27.4256i	0.0894494	−	0.215950i	−0.872824	−	0.488036i	$-0.837714\pi$
$127$	11.3601	−	27.4256i	0.0894494	−	0.215950i	0.962273	+	0.272086i	$0.0877135\pi$
$128$		0			0
$129$	−45.8221	+	68.5776i	−0.355210	+	0.531609i
$130$		0			0
$131$	66.9867	+	100.253i	0.511349	+	0.765288i	0.993865	−	0.110599i	$-0.0352771\pi$
$131$	66.9867	+	100.253i	0.511349	+	0.765288i	−0.482516	+	0.875887i	$0.660277\pi$
$132$		0			0
$133$	142.550	+	28.3549i	1.07180	+	0.213195i
$134$		0			0
$135$		−	142.063i		−	1.05232i
$136$		0			0
$137$	199.273			1.45455			0.727274	−	0.686347i	$-0.240787\pi$
$137$	199.273			1.45455			0.727274	+	0.686347i	$0.240787\pi$
$138$		0			0
$139$	−46.3445	+	232.990i	−0.333414	+	1.67619i	0.342744	+	0.939429i	$0.388644\pi$
$139$	−46.3445	+	232.990i	−0.333414	+	1.67619i	−0.676158	+	0.736757i	$0.736356\pi$
$140$		0			0
$141$	129.902	−	86.7976i	0.921289	−	0.615585i
$142$		0			0
$143$	143.471	+	95.8643i	1.00329	+	0.670380i
$144$		0			0
$145$	33.5691	+	13.9048i	0.231511	+	0.0958951i
$146$		0			0
$147$	2.77095	−	0.551177i	0.0188500	−	0.00374950i
$148$		0			0
$149$	171.865	+	171.865i	1.15346	+	1.15346i	0.985854	+	0.167605i	$0.0536033\pi$
$149$	171.865	+	171.865i	1.15346	+	1.15346i	0.167605	+	0.985854i	$0.446397\pi$
$150$		0			0
$151$	−83.7459	−	202.181i	−0.554609	−	1.33894i	−0.913984	−	0.405751i	$-0.867010\pi$
$151$	−83.7459	−	202.181i	−0.554609	−	1.33894i	0.359375	−	0.933193i	$-0.382990\pi$
$152$		0			0
$153$	18.8811	+	17.5006i	0.123406	+	0.114383i
$154$		0			0
$155$	−58.9380	+	24.4129i	−0.380245	+	0.157503i
$156$		0			0
$157$	4.38222	−	4.38222i	0.0279122	−	0.0279122i	−0.693013	−	0.720925i	$-0.743717\pi$
$157$	4.38222	−	4.38222i	0.0279122	−	0.0279122i	0.720925	+	0.693013i	$0.243717\pi$
$158$		0			0
$159$	31.6538	+	159.134i	0.199080	+	1.00084i
$160$		0			0
$161$	60.6214	−	146.353i	0.376530	−	0.909025i
$162$		0			0
$163$	154.629	−	231.418i	0.948641	−	1.41974i	0.0413945	−	0.999143i	$-0.486820\pi$
$163$	154.629	−	231.418i	0.948641	−	1.41974i	0.907247	−	0.420599i	$-0.138180\pi$
$164$		0			0
$165$	108.939	+	163.039i	0.660239	+	0.988117i
$166$		0			0
$167$	140.876	+	28.0219i	0.843567	+	0.167796i	0.597912	−	0.801562i	$-0.295997\pi$
$167$	140.876	+	28.0219i	0.843567	+	0.167796i	0.245655	+	0.969357i	$0.420997\pi$
$168$		0			0
$169$		−	27.6352i		−	0.163522i
$170$		0			0
$171$	−31.7798			−0.185847
$172$		0			0
$173$	−24.0963	+	121.140i	−0.139285	+	0.700232i	0.846523	+	0.532353i	$0.178692\pi$
$173$	−24.0963	+	121.140i	−0.139285	+	0.700232i	−0.985808	+	0.167879i	$0.946308\pi$
$174$		0			0
$175$	3.52665	−	2.35643i	0.0201523	−	0.0134653i
$176$		0			0
$177$	−16.7276	−	11.1770i	−0.0945062	−	0.0631470i
$178$		0			0
$179$	56.6975	+	23.4849i	0.316746	+	0.131200i	0.535392	−	0.844604i	$-0.320164\pi$
$179$	56.6975	+	23.4849i	0.316746	+	0.131200i	−0.218646	+	0.975804i	$0.570164\pi$
$180$		0			0
$181$	−130.086	+	25.8757i	−0.718708	+	0.142960i	−0.540878	−	0.841101i	$-0.681908\pi$
$181$	−130.086	+	25.8757i	−0.718708	+	0.142960i	−0.177830	+	0.984061i	$0.556908\pi$
$182$		0			0
$183$	−156.916	−	156.916i	−0.857462	−	0.857462i
$184$		0			0
$185$	−19.4554	−	46.9695i	−0.105164	−	0.253889i
$186$		0			0
$187$	−243.626	−	38.9216i	−1.30281	−	0.208137i
$188$		0			0
$189$	184.071	−	76.2448i	0.973921	−	0.403411i
$190$		0			0
$191$	−59.9298	+	59.9298i	−0.313768	+	0.313768i	−0.846368	−	0.532599i	$-0.821215\pi$
$191$	−59.9298	+	59.9298i	−0.313768	+	0.313768i	0.532599	+	0.846368i	$0.321215\pi$
$192$		0			0
$193$	−50.7736	−	255.256i	−0.263075	−	1.32257i	−0.855860	−	0.517208i	$-0.826971\pi$
$193$	−50.7736	−	255.256i	−0.263075	−	1.32257i	0.592784	−	0.805361i	$-0.298029\pi$
$194$		0			0
$195$	−61.4765	+	148.417i	−0.315264	+	0.761115i
$196$		0			0
$197$	88.2444	−	132.067i	0.447941	−	0.670391i	−0.536940	−	0.843620i	$-0.680420\pi$
$197$	88.2444	−	132.067i	0.447941	−	0.670391i	0.984882	+	0.173229i	$0.0554200\pi$
$198$		0			0
$199$	71.6775	+	107.273i	0.360188	+	0.539060i	0.966666	−	0.256041i	$-0.0824181\pi$
$199$	71.6775	+	107.273i	0.360188	+	0.539060i	−0.606478	+	0.795100i	$0.707418\pi$
$200$		0			0
$201$	156.623	+	31.1542i	0.779217	+	0.154996i
$202$		0			0
$203$			50.9581i			0.251025i
$204$		0			0
$205$	−357.879			−1.74575
$206$		0			0
$207$	−6.75741	+	33.9718i	−0.0326445	+	0.164115i
$208$		0			0
$209$	253.229	−	169.202i	1.21162	−	0.809579i
$210$		0			0
$211$	34.2584	+	22.8907i	0.162362	+	0.108487i	0.634097	−	0.773254i	$-0.281372\pi$
$211$	34.2584	+	22.8907i	0.162362	+	0.108487i	−0.471735	+	0.881740i	$0.656372\pi$
$212$		0			0
$213$	28.5793	+	11.8380i	0.134175	+	0.0555772i
$214$		0			0
$215$	−146.009	+	29.0430i	−0.679112	+	0.135084i
$216$		0			0
$217$	−63.2636	−	63.2636i	−0.291537	−	0.291537i
$218$		0			0
$219$	−76.5325	−	184.766i	−0.349463	−	0.843679i
$220$		0			0
$221$	−84.3752	−	183.672i	−0.381788	−	0.831093i
$222$		0			0
$223$	−8.19037	+	3.39256i	−0.0367281	+	0.0152133i	−0.400972	−	0.916090i	$-0.631328\pi$
$223$	−8.19037	+	3.39256i	−0.0367281	+	0.0152133i	0.364244	+	0.931304i	$0.381328\pi$
$224$		0			0
$225$	−0.655782	+	0.655782i	−0.00291459	+	0.00291459i
$226$		0			0
$227$	19.4704	+	97.8842i	0.0857726	+	0.431208i	0.999680	+	0.0252858i	$0.00804959\pi$
$227$	19.4704	+	97.8842i	0.0857726	+	0.431208i	−0.913908	+	0.405922i	$0.866950\pi$
$228$		0			0
$229$	−142.778	+	344.697i	−0.623485	+	1.50523i	0.224100	+	0.974566i	$0.428056\pi$
$229$	−142.778	+	344.697i	−0.623485	+	1.50523i	−0.847585	+	0.530660i	$0.821944\pi$
$230$		0			0
$231$	−152.782	+	228.655i	−0.661396	+	0.989849i
$232$		0			0
$233$	156.473	+	234.179i	0.671559	+	1.00506i	0.998204	+	0.0599121i	$0.0190821\pi$
$233$	156.473	+	234.179i	0.671559	+	1.00506i	−0.326644	+	0.945147i	$0.605918\pi$
$234$		0			0
$235$	276.575	+	55.0142i	1.17691	+	0.234103i
$236$		0			0
$237$		−	267.225i		−	1.12753i
$238$		0			0
$239$	−267.067			−1.11744			−0.558719	−	0.829357i	$-0.688707\pi$
$239$	−267.067			−1.11744			−0.558719	+	0.829357i	$0.688707\pi$
$240$		0			0
$241$	−72.0613	+	362.277i	−0.299010	+	1.50322i	0.480591	+	0.876945i	$0.340422\pi$
$241$	−72.0613	+	362.277i	−0.299010	+	1.50322i	−0.779600	+	0.626278i	$0.784578\pi$
$242$		0			0
$243$	−67.2274	+	44.9199i	−0.276656	+	0.184856i
$244$		0			0
$245$	4.24006	+	2.83312i	0.0173064	+	0.0115637i
$246$		0			0
$247$	230.518	+	95.4838i	0.933272	+	0.386574i
$248$		0			0
$249$	−217.456	+	43.2547i	−0.873317	+	0.173714i
$250$		0			0
$251$	−204.089	−	204.089i	−0.813105	−	0.813105i	0.171993	−	0.985098i	$-0.444979\pi$
$251$	−204.089	−	204.089i	−0.813105	−	0.813105i	−0.985098	+	0.171993i	$0.944979\pi$
$252$		0			0
$253$	−127.028	−	306.673i	−0.502088	−	1.21215i
$254$		0			0
$255$	−8.70981	−	229.528i	−0.0341561	−	0.900109i
$256$		0			0
$257$	−105.828	+	43.8353i	−0.411781	+	0.170565i	−0.578950	−	0.815363i	$-0.696537\pi$
$257$	−105.828	+	43.8353i	−0.411781	+	0.170565i	0.167169	+	0.985928i	$0.446537\pi$
$258$		0			0
$259$	50.4167	−	50.4167i	0.194659	−	0.194659i
$260$		0			0
$261$	−2.17374	−	10.9281i	−0.00832850	−	0.0418702i
$262$		0			0
$263$	−179.470	+	433.279i	−0.682396	+	1.64745i	0.0771690	+	0.997018i	$0.475412\pi$
$263$	−179.470	+	433.279i	−0.682396	+	1.64745i	−0.759565	+	0.650431i	$0.774588\pi$
$264$		0			0
$265$	−162.704	+	243.504i	−0.613978	+	0.918883i
$266$		0			0
$267$	−252.991	−	378.628i	−0.947531	−	1.41808i
$268$		0			0
$269$	−362.635	−	72.1325i	−1.34808	−	0.268151i	−0.532324	−	0.846541i	$-0.678681\pi$
$269$	−362.635	−	72.1325i	−1.34808	−	0.268151i	−0.815760	+	0.578390i	$0.803681\pi$
$270$		0			0
$271$			391.001i			1.44281i	0.692515	+	0.721404i	$0.256503\pi$
$271$			391.001i			1.44281i	−0.692515	+	0.721404i	$0.743497\pi$
$272$		0			0
$273$	−225.298			−0.825268
$274$		0			0
$275$	1.73391	−	8.71695i	0.00630512	−	0.0316980i
$276$		0			0
$277$	245.566	−	164.082i	0.886520	−	0.592354i	−0.0267802	−	0.999641i	$-0.508525\pi$
$277$	245.566	−	164.082i	0.886520	−	0.592354i	0.913300	+	0.407288i	$0.133525\pi$
$278$		0			0
$279$	16.2657	+	10.8684i	0.0583001	+	0.0389549i
$280$		0			0
$281$	266.219	+	110.271i	0.947398	+	0.392425i	0.802252	−	0.596985i	$-0.203635\pi$
$281$	266.219	+	110.271i	0.947398	+	0.392425i	0.145146	+	0.989410i	$0.453635\pi$
$282$		0			0
$283$	484.407	−	96.3544i	1.71168	−	0.340475i	0.760556	−	0.649272i	$-0.224926\pi$
$283$	484.407	−	96.3544i	1.71168	−	0.340475i	0.951128	+	0.308797i	$0.0999265\pi$
$284$		0			0
$285$	200.495	+	200.495i	0.703490	+	0.703490i
$286$		0			0
$287$	−192.072	−	463.703i	−0.669241	−	1.61569i
$288$		0			0
$289$	219.253	+	188.279i	0.758661	+	0.651486i
$290$		0			0
$291$	315.339	−	130.618i	1.08364	−	0.448858i
$292$		0			0
$293$	−253.865	+	253.865i	−0.866434	+	0.866434i	−0.992076	−	0.125642i	$-0.959901\pi$
$293$	−253.865	+	253.865i	−0.866434	+	0.866434i	0.125642	+	0.992076i	$0.459901\pi$
$294$		0			0
$295$	−7.08424	−	35.6149i	−0.0240144	−	0.120728i
$296$		0			0
$297$	159.766	−	385.709i	0.537933	−	1.29868i
$298$		0			0
$299$	151.086	−	226.115i	0.505303	−	0.756239i
$300$		0			0
$301$	−115.993	−	173.596i	−0.385360	−	0.576732i
$302$		0			0
$303$	222.184	+	44.1952i	0.733282	+	0.145859i
$304$		0			0
$305$		−	400.545i		−	1.31326i
$306$		0			0
$307$	316.326			1.03038			0.515190	−	0.857076i	$-0.327722\pi$
$307$	316.326			1.03038			0.515190	+	0.857076i	$0.327722\pi$
$308$		0			0
$309$	−85.5399	+	430.038i	−0.276828	+	1.39171i
$310$		0			0
$311$	−42.9880	+	28.7236i	−0.138225	+	0.0923589i	−0.622760	−	0.782413i	$-0.713989\pi$
$311$	−42.9880	+	28.7236i	−0.138225	+	0.0923589i	0.484535	+	0.874772i	$0.338989\pi$
$312$		0			0
$313$	−152.315	−	101.774i	−0.486630	−	0.325156i	0.287935	−	0.957650i	$-0.407031\pi$
$313$	−152.315	−	101.774i	−0.486630	−	0.325156i	−0.774565	+	0.632494i	$0.782031\pi$
$314$		0			0
$315$	47.8525	+	19.8211i	0.151913	+	0.0629242i
$316$		0			0
$317$	−202.581	+	40.2959i	−0.639057	+	0.127116i	−0.503975	−	0.863718i	$-0.668130\pi$
$317$	−202.581	+	40.2959i	−0.639057	+	0.127116i	−0.135082	+	0.990834i	$0.543130\pi$
$318$		0			0
$319$	75.5045	+	75.5045i	0.236691	+	0.236691i
$320$		0			0
$321$	74.6414	+	180.200i	0.232528	+	0.561371i
$322$		0			0
$323$	−356.497	+	13.5279i	−1.10371	+	0.0418819i
$324$		0			0
$325$	6.72712	−	2.78646i	0.0206988	−	0.00857374i
$326$		0			0
$327$	190.296	−	190.296i	0.581946	−	0.581946i
$328$		0			0
$329$	77.1548	+	387.883i	0.234513	+	1.17898i
$330$		0			0
$331$	92.7388	−	223.891i	0.280178	−	0.676409i	−0.719662	−	0.694325i	$-0.755703\pi$
$331$	92.7388	−	223.891i	0.280178	−	0.676409i	0.999839	+	0.0179161i	$0.00570317\pi$
$332$		0			0
$333$	−8.66138	+	12.9627i	−0.0260101	+	0.0389269i
$334$		0			0
$335$	160.136	+	239.661i	0.478019	+	0.715406i
$336$		0			0
$337$	3.26659	+	0.649766i	0.00969316	+	0.00192809i	0.199935	−	0.979809i	$-0.435927\pi$
$337$	3.26659	+	0.649766i	0.00969316	+	0.00192809i	−0.190241	+	0.981737i	$0.560927\pi$
$338$		0			0
$339$		−	397.918i		−	1.17380i
$340$		0			0
$341$	−187.475			−0.549780
$342$		0			0
$343$	−67.6024	+	339.860i	−0.197091	+	0.990846i
$344$		0			0
$345$	256.956	−	171.692i	0.744799	−	0.497659i
$346$		0			0
$347$	98.4746	+	65.7986i	0.283788	+	0.189621i	0.689315	−	0.724462i	$-0.257912\pi$
$347$	98.4746	+	65.7986i	0.283788	+	0.189621i	−0.405526	+	0.914083i	$0.632912\pi$
$348$		0			0
$349$	543.732	+	225.221i	1.55797	+	0.645333i	0.984736	−	0.174057i	$-0.0556878\pi$
$349$	543.732	+	225.221i	1.55797	+	0.645333i	0.573236	+	0.819390i	$0.305688\pi$
$350$		0			0
$351$	335.461	−	66.7273i	0.955729	−	0.190106i
$352$		0			0
$353$	−291.213	−	291.213i	−0.824966	−	0.824966i	0.161850	−	0.986815i	$-0.448254\pi$
$353$	−291.213	−	291.213i	−0.824966	−	0.824966i	−0.986815	+	0.161850i	$0.948254\pi$
$354$		0			0
$355$	21.3672	+	51.5849i	0.0601892	+	0.145310i
$356$		0			0
$357$	292.724	−	134.472i	0.819956	−	0.376672i
$358$		0			0
$359$	−42.1392	+	17.4546i	−0.117379	+	0.0486202i	−0.440600	−	0.897703i	$-0.645234\pi$
$359$	−42.1392	+	17.4546i	−0.117379	+	0.0486202i	0.323221	+	0.946324i	$0.395234\pi$
$360$		0			0
$361$	56.1379	−	56.1379i	0.155507	−	0.155507i
$362$		0			0
$363$	47.8347	+	240.482i	0.131776	+	0.662483i
$364$		0			0
$365$	138.139	−	333.497i	0.378463	−	0.913690i
$366$		0			0
$367$	113.046	−	169.186i	0.308028	−	0.460997i	−0.644868	−	0.764294i	$-0.723088\pi$
$367$	113.046	−	169.186i	0.308028	−	0.460997i	0.952896	+	0.303297i	$0.0980875\pi$
$368$		0			0
$369$	60.9708	+	91.2493i	0.165233	+	0.247288i
$370$		0			0
$371$	−402.831	−	80.1280i	−1.08580	−	0.215978i
$372$		0			0
$373$			384.052i			1.02963i	0.857301	+	0.514815i	$0.172139\pi$
$373$			384.052i			1.02963i	−0.857301	+	0.514815i	$0.827861\pi$
$374$		0			0
$375$	346.058			0.922822
$376$		0			0
$377$	−17.0666	+	85.7995i	−0.0452695	+	0.227585i
$378$		0			0
$379$	106.040	−	70.8535i	0.279788	−	0.186949i	−0.407756	−	0.913091i	$-0.633689\pi$
$379$	106.040	−	70.8535i	0.279788	−	0.186949i	0.687544	+	0.726142i	$0.258689\pi$
$380$		0			0
$381$	67.5308	+	45.1226i	0.177246	+	0.118432i
$382$		0			0
$383$	−30.5334	−	12.6473i	−0.0797216	−	0.0330218i	0.342466	−	0.939530i	$-0.388738\pi$
$383$	−30.5334	−	12.6473i	−0.0797216	−	0.0330218i	−0.422188	+	0.906508i	$0.638738\pi$
$384$		0			0
$385$	−486.832	+	96.8368i	−1.26450	+	0.251524i
$386$		0			0
$387$	32.2803	+	32.2803i	0.0834117	+	0.0834117i
$388$		0			0
$389$	230.298	+	555.989i	0.592027	+	1.42928i	0.881542	+	0.472105i	$0.156506\pi$
$389$	230.298	+	555.989i	0.592027	+	1.42928i	−0.289515	+	0.957173i	$0.593494\pi$
$390$		0			0
$391$	−61.3419	+	383.963i	−0.156885	+	0.982003i
$392$		0			0
$393$	−304.775	+	126.242i	−0.775509	+	0.321226i
$394$		0			0
$395$	341.061	−	341.061i	0.863445	−	0.863445i
$396$		0			0
$397$	−105.476	−	530.265i	−0.265683	−	1.33568i	−0.851124	−	0.524964i	$-0.824079\pi$
$397$	−105.476	−	530.265i	−0.265683	−	1.33568i	0.585441	−	0.810715i	$-0.300921\pi$
$398$		0			0
$399$	−152.176	+	367.385i	−0.381393	+	0.920765i
$400$		0			0
$401$	96.8102	−	144.887i	0.241422	−	0.361314i	−0.690895	−	0.722955i	$-0.742783\pi$
$401$	96.8102	−	144.887i	0.241422	−	0.361314i	0.932317	+	0.361641i	$0.117783\pi$
$402$		0			0
$403$	−85.3307	−	127.706i	−0.211739	−	0.316889i
$404$		0			0
$405$	315.202	+	62.6975i	0.778276	+	0.154809i
$406$		0			0
$407$		−	149.405i		−	0.367087i
$408$		0			0
$409$	175.287			0.428575			0.214287	−	0.976771i	$-0.431257\pi$
$409$	175.287			0.428575			0.214287	+	0.976771i	$0.431257\pi$
$410$		0			0
$411$	−106.365	+	534.733i	−0.258795	+	1.30105i
$412$		0			0
$413$	42.3441	−	28.2934i	0.102528	−	0.0685070i
$414$		0			0
$415$	−332.747	−	222.334i	−0.801800	−	0.535746i
$416$		0			0
$417$	−600.472	−	248.723i	−1.43998	−	0.596459i
$418$		0			0
$419$	16.7112	−	3.32406i	0.0398835	−	0.00793332i	−0.175108	−	0.984549i	$-0.556028\pi$
$419$	16.7112	−	3.32406i	0.0398835	−	0.00793332i	0.214992	+	0.976616i	$0.431028\pi$
$420$		0			0
$421$	−250.003	−	250.003i	−0.593832	−	0.593832i	0.344832	−	0.938664i	$-0.387936\pi$
$421$	−250.003	−	250.003i	−0.593832	−	0.593832i	−0.938664	+	0.344832i	$0.887936\pi$
$422$		0			0
$423$	−33.0922	−	79.8916i	−0.0782321	−	0.188869i
$424$		0			0
$425$	−7.07724	+	7.63554i	−0.0166523	+	0.0179660i
$426$		0			0
$427$	518.985	−	214.971i	1.21542	−	0.503444i
$428$		0			0
$429$	−333.824	+	333.824i	−0.778144	+	0.778144i
$430$		0			0
$431$	91.8846	+	461.935i	0.213189	+	1.07178i	0.928035	+	0.372493i	$0.121497\pi$
$431$	91.8846	+	461.935i	0.213189	+	1.07178i	−0.714846	+	0.699282i	$0.753503\pi$
$432$		0			0
$433$	132.218	−	319.203i	0.305354	−	0.737190i	−0.694489	−	0.719503i	$-0.744370\pi$
$433$	132.218	−	319.203i	0.305354	−	0.737190i	0.999844	−	0.0176873i	$-0.00563034\pi$
$434$		0			0
$435$	−55.2304	+	82.6581i	−0.126966	+	0.190019i
$436$		0			0
$437$	−266.668	−	399.097i	−0.610225	−	0.913266i
$438$		0			0
$439$	167.954	+	33.4082i	0.382584	+	0.0761007i	0.382636	−	0.923899i	$-0.375016\pi$
$439$	167.954	+	33.4082i	0.382584	+	0.0761007i	−5.15940e−5		1.00000i	$0.500016\pi$
$440$		0			0
$441$		−	1.56377i		−	0.00354596i
$442$		0			0
$443$	−326.061			−0.736030			−0.368015	−	0.929820i	$-0.619963\pi$
$443$	−326.061			−0.736030			−0.368015	+	0.929820i	$0.619963\pi$
$444$		0			0
$445$	160.351	−	806.139i	0.360339	−	1.81155i
$446$		0			0
$447$	−552.922	+	369.451i	−1.23696	+	0.826512i
$448$		0			0
$449$	−304.299	−	203.326i	−0.677725	−	0.452842i	0.168475	−	0.985706i	$-0.446116\pi$
$449$	−304.299	−	203.326i	−0.677725	−	0.452842i	−0.846201	+	0.532864i	$0.821116\pi$
$450$		0			0
$451$	−971.660	−	402.475i	−2.15446	−	0.892406i
$452$		0			0
$453$	587.235	−	116.808i	1.29633	−	0.257855i
$454$		0			0
$455$	−287.550	−	287.550i	−0.631978	−	0.631978i
$456$		0			0
$457$	234.142	+	565.268i	0.512345	+	1.23691i	0.942516	+	0.334162i	$0.108453\pi$
$457$	234.142	+	565.268i	0.512345	+	1.23691i	−0.430171	+	0.902748i	$0.641547\pi$
$458$		0			0
$459$	−396.029	+	286.921i	−0.862808	+	0.625100i
$460$		0			0
$461$	−208.899	+	86.5290i	−0.453144	+	0.187698i	−0.597569	−	0.801817i	$-0.703867\pi$
$461$	−208.899	+	86.5290i	−0.453144	+	0.187698i	0.144425	+	0.989516i	$0.453867\pi$
$462$		0			0
$463$	−411.627	+	411.627i	−0.889042	+	0.889042i	−0.994431	−	0.105389i	$-0.966391\pi$
$463$	−411.627	+	411.627i	−0.889042	+	0.889042i	0.105389	+	0.994431i	$0.466391\pi$
$464$		0			0
$465$	−34.0510	−	171.186i	−0.0732280	−	0.368142i
$466$		0			0
$467$	54.7906	−	132.276i	0.117325	−	0.283247i	−0.854298	−	0.519784i	$-0.826012\pi$
$467$	54.7906	−	132.276i	0.117325	−	0.283247i	0.971622	+	0.236537i	$0.0760125\pi$
$468$		0			0
$469$	−224.584	+	336.113i	−0.478857	+	0.716659i
$470$		0			0
$471$	9.42025	+	14.0984i	0.0200005	+	0.0299329i
$472$		0			0
$473$	−429.084	−	85.3502i	−0.907155	−	0.180444i
$474$		0			0
$475$		−	12.8518i		−	0.0270563i
$476$		0			0
$477$	89.8063			0.188273
$478$		0			0
$479$	182.078	−	915.368i	0.380121	−	1.91100i	−0.0312143	−	0.999513i	$-0.509937\pi$
$479$	182.078	−	915.368i	0.380121	−	1.91100i	0.411335	−	0.911484i	$-0.365063\pi$
$480$		0			0
$481$	101.773	−	68.0027i	0.211587	−	0.141378i
$482$		0			0
$483$	360.369	+	240.791i	0.746105	+	0.498531i
$484$		0			0
$485$	569.178	+	235.761i	1.17356	+	0.486105i
$486$		0			0
$487$	−652.204	+	129.731i	−1.33923	+	0.266389i	−0.812160	−	0.583435i	$-0.801708\pi$
$487$	−652.204	+	129.731i	−1.33923	+	0.266389i	−0.527067	+	0.849824i	$0.676708\pi$
$488$		0			0
$489$	538.456	+	538.456i	1.10114	+	1.10114i
$490$		0			0
$491$	−53.4434	−	129.024i	−0.108846	−	0.262778i	0.860066	−	0.510183i	$-0.170422\pi$
$491$	−53.4434	−	129.024i	−0.108846	−	0.262778i	−0.968912	+	0.247405i	$0.920422\pi$
$492$		0			0
$493$	−29.0363	−	121.663i	−0.0588971	−	0.246782i
$494$		0			0
$495$	100.272	−	41.5339i	0.202569	−	0.0839069i
$496$		0			0
$497$	−55.3708	+	55.3708i	−0.111410	+	0.111410i
$498$		0			0
$499$	−35.4107	−	178.022i	−0.0709633	−	0.356757i	0.928946	−	0.370215i	$-0.120716\pi$
$499$	−35.4107	−	178.022i	−0.0709633	−	0.356757i	−0.999909	+	0.0134583i	$0.995716\pi$
$500$		0			0
$501$	−150.389	+	363.071i	−0.300178	+	0.724693i
$502$		0			0
$503$	−309.416	+	463.074i	−0.615141	+	0.920623i	−0.999997	−	0.00235306i	$-0.999251\pi$
$503$	−309.416	+	463.074i	−0.615141	+	0.920623i	0.384856	+	0.922976i	$0.374251\pi$
$504$		0			0
$505$	227.169	+	339.982i	0.449839	+	0.673232i
$506$		0			0
$507$	74.1568	+	14.7507i	0.146266	+	0.0290941i
$508$		0			0
$509$			471.896i			0.927105i	0.886070	+	0.463552i	$0.153425\pi$
$509$			471.896i			0.927105i	−0.886070	+	0.463552i	$0.846575\pi$
$510$		0			0
$511$	506.250			0.990704
$512$		0			0
$513$	117.775	−	592.094i	0.229580	−	1.15418i
$514$		0			0
$515$	−658.036	+	439.686i	−1.27774	+	0.853758i
$516$		0			0
$517$	689.046	+	460.406i	1.33278	+	0.890533i
$518$		0			0
$519$	−312.208	−	129.321i	−0.601556	−	0.249173i
$520$		0			0
$521$	−354.841	+	70.5823i	−0.681077	+	0.135475i	−0.523492	−	0.852031i	$-0.675371\pi$
$521$	−354.841	+	70.5823i	−0.681077	+	0.135475i	−0.157585	+	0.987505i	$0.550371\pi$
$522$		0			0
$523$	367.394	+	367.394i	0.702474	+	0.702474i	0.964941	−	0.262467i	$-0.0845361\pi$
$523$	367.394	+	367.394i	0.702474	+	0.702474i	−0.262467	+	0.964941i	$0.584536\pi$
$524$		0			0
$525$	4.44089	+	10.7213i	0.00845884	+	0.0204214i
$526$		0			0
$527$	187.091	+	114.995i	0.355011	+	0.218207i
$528$		0			0
$529$	5.40430	−	2.23854i	0.0102161	−	0.00423164i
$530$		0			0
$531$	−7.87389	+	7.87389i	−0.0148284	+	0.0148284i
$532$		0			0
$533$	−168.096	−	845.077i	−0.315378	−	1.58551i
$534$		0			0
$535$	−134.726	+	325.256i	−0.251823	+	0.607955i
$536$		0			0
$537$	−93.2828	+	139.608i	−0.173711	+	0.259977i
$538$		0			0
$539$	8.32582	+	12.4605i	0.0154468	+	0.0231178i
$540$		0			0
$541$	60.1102	+	11.9567i	0.111110	+	0.0221011i	0.250332	−	0.968160i	$-0.419460\pi$
$541$	60.1102	+	11.9567i	0.111110	+	0.0221011i	−0.139222	+	0.990261i	$0.544460\pi$
$542$		0			0
$543$		−	362.887i		−	0.668300i
$544$		0			0
$545$	485.753			0.891290
$546$		0			0
$547$	104.771	−	526.720i	0.191538	−	0.962925i	−0.758710	−	0.651429i	$-0.774170\pi$
$547$	104.771	−	526.720i	0.191538	−	0.962925i	0.950247	−	0.311496i	$-0.100830\pi$
$548$		0			0
$549$	−102.128	+	68.2397i	−0.186025	+	0.124298i
$550$		0			0
$551$	128.383	+	85.7825i	0.232999	+	0.155685i
$552$		0			0
$553$	624.958	+	258.866i	1.13012	+	0.468112i
$554$		0			0
$555$	136.423	−	27.1363i	0.245808	−	0.0488943i
$556$		0			0
$557$	−247.961	−	247.961i	−0.445172	−	0.445172i	0.448574	−	0.893746i	$-0.351932\pi$
$557$	−247.961	−	247.961i	−0.445172	−	0.445172i	−0.893746	+	0.448574i	$0.851932\pi$
$558$		0			0
$559$	−137.161	−	331.137i	−0.245369	−	0.592373i
$560$		0			0
$561$	234.482	−	632.975i	0.417971	−	1.12830i
$562$		0			0
$563$	−459.110	+	190.169i	−0.815470	+	0.337779i	−0.751134	−	0.660150i	$-0.770493\pi$
$563$	−459.110	+	190.169i	−0.815470	+	0.337779i	−0.0643359	+	0.997928i	$0.520493\pi$
$564$		0			0
$565$	507.866	−	507.866i	0.898878	−	0.898878i
$566$		0			0
$567$	87.9303	+	442.056i	0.155080	+	0.779640i
$568$		0			0
$569$	78.5172	−	189.557i	0.137992	−	0.333141i	−0.839744	−	0.542983i	$-0.817295\pi$
$569$	78.5172	−	189.557i	0.137992	−	0.333141i	0.977735	+	0.209842i	$0.0672948\pi$
$570$		0			0
$571$	583.483	−	873.244i	1.02186	−	1.52932i	0.184382	−	0.982855i	$-0.440972\pi$
$571$	583.483	−	873.244i	1.02186	−	1.52932i	0.837479	−	0.546469i	$-0.184028\pi$
$572$		0			0
$573$	−128.828	−	192.805i	−0.224831	−	0.336483i
$574$		0			0
$575$	−13.7382	−	2.73270i	−0.0238926	−	0.00475252i
$576$		0			0
$577$		−	48.0445i		−	0.0832660i	−0.999133	−	0.0416330i	$-0.986744\pi$
$577$		−	48.0445i		−	0.0832660i	0.999133	−	0.0416330i	$-0.0132560\pi$
$578$		0			0
$579$	712.059			1.22981
$580$		0			0
$581$	109.494	−	550.466i	0.188459	−	0.947445i
$582$		0			0
$583$	−715.598	+	478.147i	−1.22744	+	0.820150i
$584$		0			0
$585$	73.9321	+	49.3998i	0.126380	+	0.0844442i
$586$		0			0
$587$	−172.424	−	71.4205i	−0.293738	−	0.121670i	0.230948	−	0.972966i	$-0.425817\pi$
$587$	−172.424	−	71.4205i	−0.293738	−	0.121670i	−0.524686	+	0.851296i	$0.675817\pi$
$588$		0			0
$589$	−265.882	+	52.8872i	−0.451413	+	0.0897915i
$590$		0			0
$591$	307.289	+	307.289i	0.519948	+	0.519948i
$592$		0			0
$593$	202.486	+	488.845i	0.341461	+	0.824360i	0.997569	+	0.0696924i	$0.0222018\pi$
$593$	202.486	+	488.845i	0.341461	+	0.824360i	−0.656107	+	0.754667i	$0.727798\pi$
$594$		0			0
$595$	545.233	+	201.979i	0.916359	+	0.339460i
$596$		0			0
$597$	−326.117	+	135.082i	−0.546259	+	0.226268i
$598$		0			0
$599$	536.133	−	536.133i	0.895046	−	0.895046i	−0.0999468	−	0.994993i	$-0.531867\pi$
$599$	536.133	−	536.133i	0.895046	−	0.895046i	0.994993	+	0.0999468i	$0.0318673\pi$
$600$		0			0
$601$	−66.3064	−	333.345i	−0.110327	−	0.554650i	−0.995924	−	0.0901962i	$-0.971251\pi$
$601$	−66.3064	−	333.345i	−0.110327	−	0.554650i	0.885597	−	0.464454i	$-0.153749\pi$
$602$		0			0
$603$	33.8250	−	81.6607i	0.0560945	−	0.135424i
$604$		0			0
$605$	−245.876	+	367.980i	−0.406407	+	0.608232i
$606$		0			0
$607$	206.154	+	308.532i	0.339628	+	0.508290i	0.961491	−	0.274837i	$-0.0886238\pi$
$607$	206.154	+	308.532i	0.339628	+	0.508290i	−0.621863	+	0.783126i	$0.713624\pi$
$608$		0			0
$609$	−136.742	−	27.1997i	−0.224535	−	0.0446628i
$610$		0			0
$611$			678.930i			1.11118i
$612$		0			0
$613$	−909.556			−1.48378			−0.741889	−	0.670523i	$-0.766070\pi$
$613$	−909.556			−1.48378			−0.741889	+	0.670523i	$0.766070\pi$
$614$		0			0
$615$	191.023	−	960.339i	0.310607	−	1.56153i
$616$		0			0
$617$	81.6968	−	54.5881i	0.132410	−	0.0884734i	−0.487601	−	0.873066i	$-0.662128\pi$
$617$	81.6968	−	54.5881i	0.132410	−	0.0884734i	0.620011	+	0.784593i	$0.287128\pi$
$618$		0			0
$619$	−491.587	−	328.468i	−0.794162	−	0.530642i	0.0910407	−	0.995847i	$-0.470981\pi$
$619$	−491.587	−	328.468i	−0.794162	−	0.530642i	−0.885203	+	0.465205i	$0.845981\pi$
$620$		0			0
$621$	−607.891	−	251.797i	−0.978891	−	0.405470i
$622$		0			0
$623$	1130.57	−	224.885i	1.81472	−	0.360971i
$624$		0			0
$625$	430.851	+	430.851i	0.689361	+	0.689361i
$626$		0			0
$627$	318.875	+	769.832i	0.508573	+	1.22780i
$628$		0			0
$629$	−91.6431	+	149.099i	−0.145697	+	0.237041i
$630$		0			0
$631$	126.757	−	52.5043i	0.200882	−	0.0832081i	−0.279974	−	0.960008i	$-0.590326\pi$
$631$	126.757	−	52.5043i	0.200882	−	0.0832081i	0.480856	+	0.876799i	$0.340326\pi$
$632$		0			0
$633$	−79.7112	+	79.7112i	−0.125926	+	0.125926i
$634$		0			0
$635$	28.5997	+	143.780i	0.0450389	+	0.226426i
$636$		0			0
$637$	−4.69841	+	11.3430i	−0.00737584	+	0.0178069i
$638$		0			0
$639$	9.51246	−	14.2364i	0.0148865	−	0.0222792i
$640$		0			0
$641$	−88.0571	−	131.787i	−0.137375	−	0.205596i	0.756403	−	0.654106i	$-0.226955\pi$
$641$	−88.0571	−	131.787i	−0.137375	−	0.205596i	−0.893778	+	0.448510i	$0.851955\pi$
$642$		0			0
$643$	382.860	+	76.1556i	0.595428	+	0.118438i	0.483599	−	0.875289i	$-0.339329\pi$
$643$	382.860	+	76.1556i	0.595428	+	0.118438i	0.111829	+	0.993727i	$0.464329\pi$
$644$		0			0
$645$		−	407.305i		−	0.631481i
$646$		0			0
$647$	854.713			1.32104			0.660520	−	0.750809i	$-0.270336\pi$
$647$	854.713			1.32104			0.660520	+	0.750809i	$0.270336\pi$
$648$		0			0
$649$	20.8188	−	104.663i	0.0320783	−	0.161269i
$650$		0			0
$651$	203.530	−	135.995i	0.312643	−	0.208901i
$652$		0			0
$653$	829.509	+	554.260i	1.27031	+	0.848791i	0.993687	−	0.112189i	$-0.0357862\pi$
$653$	829.509	+	554.260i	1.27031	+	0.848791i	0.276618	+	0.960980i	$0.410786\pi$
$654$		0			0
$655$	−550.110	−	227.863i	−0.839862	−	0.347882i
$656$		0			0
$657$	−108.567	+	21.5953i	−0.165246	+	0.0328696i
$658$		0			0
$659$	309.969	+	309.969i	0.470362	+	0.470362i	0.902032	−	0.431670i	$-0.142075\pi$
$659$	309.969	+	309.969i	0.470362	+	0.470362i	−0.431670	+	0.902032i	$0.642075\pi$
$660$		0			0
$661$	494.281	+	1193.30i	0.747778	+	1.80529i	0.570818	+	0.821077i	$0.306626\pi$
$661$	494.281	+	1193.30i	0.747778	+	1.80529i	0.176960	+	0.984218i	$0.443374\pi$
$662$		0			0
$663$	537.904	−	128.376i	0.811318	−	0.193630i
$664$		0			0
$665$	−663.120	+	274.673i	−0.997173	+	0.413042i
$666$		0			0
$667$	118.998	−	118.998i	0.178407	−	0.178407i
$668$		0			0
$669$	−4.73193	−	23.7890i	−0.00707314	−	0.0355591i
$670$		0			0
$671$	450.457	−	1087.50i	0.671322	−	1.62072i
$672$		0			0
$673$	460.441	−	689.099i	0.684162	−	1.02392i	−0.313082	−	0.949726i	$-0.601361\pi$
$673$	460.441	−	689.099i	0.684162	−	1.02392i	0.997244	−	0.0741946i	$-0.0236386\pi$
$674$		0			0
$675$	−9.78767	−	14.6483i	−0.0145003	−	0.0217012i
$676$		0			0
$677$	−200.597	−	39.9012i	−0.296302	−	0.0589382i	0.0447006	−	0.999000i	$-0.485767\pi$
$677$	−200.597	−	39.9012i	−0.296302	−	0.0589382i	−0.341003	+	0.940062i	$0.610767\pi$
$678$		0			0
$679$			864.015i			1.27248i
$680$		0			0
$681$	−273.057			−0.400964
$682$		0			0
$683$	−184.078	+	925.424i	−0.269514	+	1.35494i	0.574450	+	0.818540i	$0.305216\pi$
$683$	−184.078	+	925.424i	−0.269514	+	1.35494i	−0.843964	+	0.536400i	$0.819784\pi$
$684$		0			0
$685$	−818.237	+	546.729i	−1.19451	+	0.798144i
$686$		0			0
$687$	−848.755	−	567.120i	−1.23545	−	0.825502i
$688$		0			0
$689$	−651.421	−	269.827i	−0.945458	−	0.391622i
$690$		0			0
$691$	−335.709	+	66.7767i	−0.485831	+	0.0966378i	−0.431927	−	0.901908i	$-0.642166\pi$
$691$	−335.709	+	66.7767i	−0.485831	+	0.0966378i	−0.0539035	+	0.998546i	$0.517166\pi$
$692$		0			0
$693$	107.631	+	107.631i	0.155311	+	0.155311i
$694$		0			0
$695$	−448.939	−	1083.83i	−0.645955	−	1.55947i
$696$		0			0
$697$	722.797	+	997.656i	1.03701	+	1.43136i
$698$		0			0
$699$	−711.919	+	294.887i	−1.01848	+	0.421869i
$700$		0			0
$701$	42.1600	−	42.1600i	0.0601427	−	0.0601427i	−0.676396	−	0.736538i	$-0.736459\pi$
$701$	42.1600	−	42.1600i	0.0601427	−	0.0601427i	0.736538	+	0.676396i	$0.236459\pi$
$702$		0			0
$703$	−42.1475	−	211.890i	−0.0599537	−	0.301408i
$704$		0			0
$705$	−295.252	+	712.801i	−0.418797	+	1.01107i
$706$		0			0
$707$	−318.594	+	476.809i	−0.450628	+	0.674412i
$708$		0			0
$709$	−41.8111	−	62.5747i	−0.0589719	−	0.0882577i	0.800812	−	0.598916i	$-0.204402\pi$
$709$	−41.8111	−	62.5747i	−0.0589719	−	0.0882577i	−0.859784	+	0.510658i	$0.829402\pi$
$710$		0			0
$711$	−145.067	−	28.8556i	−0.204032	−	0.0405845i
$712$		0			0
$713$			295.467i			0.414400i
$714$		0			0
$715$	−852.123			−1.19178
$716$		0			0
$717$	142.551	−	716.653i	0.198816	−	0.999517i
$718$		0			0
$719$	448.524	−	299.694i	0.623816	−	0.416821i	−0.203090	−	0.979160i	$-0.565099\pi$
$719$	448.524	−	299.694i	0.623816	−	0.416821i	0.826907	+	0.562339i	$0.190099\pi$
$720$		0			0
$721$	−922.865	−	616.639i	−1.27998	−	0.855255i
$722$		0			0
$723$	−933.676	−	386.741i	−1.29139	−	0.534912i
$724$		0			0
$725$	4.41934	−	0.879061i	0.00609564	−	0.00121250i
$726$		0			0
$727$	−640.770	−	640.770i	−0.881390	−	0.881390i	0.112286	−	0.993676i	$-0.464183\pi$
$727$	−640.770	−	640.770i	−0.881390	−	0.881390i	−0.993676	+	0.112286i	$0.964183\pi$
$728$		0			0
$729$	−308.792	−	745.489i	−0.423582	−	1.02262i
$730$		0			0
$731$	375.853	+	348.371i	0.514163	+	0.476568i
$732$		0			0
$733$	464.757	−	192.509i	0.634048	−	0.262631i	−0.0424239	−	0.999100i	$-0.513508\pi$
$733$	464.757	−	192.509i	0.634048	−	0.262631i	0.676472	+	0.736468i	$0.263508\pi$
$734$		0			0
$735$	−9.86562	+	9.86562i	−0.0134226	+	0.0134226i
$736$		0			0
$737$	165.253	+	830.783i	0.224224	+	1.12725i
$738$		0			0
$739$	13.6165	−	32.8731i	0.0184256	−	0.0444832i	−0.914399	−	0.404814i	$-0.867336\pi$
$739$	13.6165	−	32.8731i	0.0184256	−	0.0444832i	0.932825	+	0.360331i	$0.117336\pi$
$740$		0			0
$741$	−379.265	+	567.611i	−0.511829	+	0.766006i
$742$		0			0
$743$	−371.138	−	555.447i	−0.499513	−	0.747574i	0.492958	−	0.870053i	$-0.335915\pi$
$743$	−371.138	−	555.447i	−0.499513	−	0.747574i	−0.992471	+	0.122479i	$0.960915\pi$
$744$		0			0
$745$	−1177.23	−	234.166i	−1.58018	−	0.314317i
$746$		0			0
$747$			122.720i			0.164284i
$748$		0			0
$749$	−493.740			−0.659200
$750$		0			0
$751$	−38.5497	+	193.802i	−0.0513312	+	0.258059i	−0.997926	−	0.0643651i	$-0.979498\pi$
$751$	−38.5497	+	193.802i	−0.0513312	+	0.258059i	0.946595	+	0.322424i	$0.104498\pi$
$752$		0			0
$753$	656.593	−	438.721i	0.871969	−	0.582631i
$754$		0			0
$755$	898.576	+	600.409i	1.19017	+	0.795244i
$756$		0			0
$757$	−273.370	−	113.234i	−0.361123	−	0.149582i	0.194742	−	0.980854i	$-0.437613\pi$
$757$	−273.370	−	113.234i	−0.361123	−	0.149582i	−0.555865	+	0.831272i	$0.687613\pi$
$758$		0			0
$759$	890.736	−	177.178i	1.17356	−	0.233437i
$760$		0			0
$761$	383.033	+	383.033i	0.503328	+	0.503328i	0.912470	−	0.409143i	$-0.134172\pi$
$761$	383.033	+	383.033i	0.503328	+	0.503328i	−0.409143	+	0.912470i	$0.634172\pi$
$762$		0			0
$763$	260.702	+	629.389i	0.341680	+	0.824888i
$764$		0			0
$765$	−125.543	−	20.0567i	−0.164108	−	0.0262179i
$766$		0			0
$767$	80.7717	−	33.4567i	0.105309	−	0.0436202i
$768$		0			0
$769$	246.685	−	246.685i	0.320787	−	0.320787i	−0.528282	−	0.849069i	$-0.677164\pi$
$769$	246.685	−	246.685i	0.320787	−	0.320787i	0.849069	+	0.528282i	$0.177164\pi$
$770$		0			0
$771$	−61.1413	−	307.378i	−0.0793013	−	0.398674i
$772$		0			0
$773$	87.7623	−	211.877i	0.113535	−	0.274097i	−0.856891	−	0.515498i	$-0.827607\pi$
$773$	87.7623	−	211.877i	0.113535	−	0.274097i	0.970425	+	0.241401i	$0.0776070\pi$
$774$		0			0
$775$	−4.39519	+	6.57787i	−0.00567122	+	0.00848757i
$776$		0			0
$777$	108.378	+	162.200i	0.139483	+	0.208751i
$778$		0			0
$779$	−1491.57	−	296.693i	−1.91473	−	0.380863i
$780$		0			0
$781$			164.085i			0.210097i
$782$		0			0
$783$	211.660			0.270319
$784$		0			0
$785$	−5.97075	+	30.0170i	−0.00760606	+	0.0382382i
$786$		0			0
$787$	−410.715	+	274.431i	−0.521874	+	0.348705i	−0.788440	−	0.615112i	$-0.789111\pi$
$787$	−410.715	+	274.431i	−0.521874	+	0.348705i	0.266566	+	0.963817i	$0.414111\pi$
$788$		0			0
$789$	−1066.87	−	712.862i	−1.35219	−	0.903501i
$790$		0			0
$791$	930.611	+	385.472i	1.17650	+	0.487322i
$792$		0			0
$793$	945.826	−	188.136i	1.19272	−	0.237247i
$794$		0			0
$795$	−566.577	−	566.577i	−0.712676	−	0.712676i
$796$		0			0
$797$	193.235	+	466.509i	0.242452	+	0.585332i	0.997525	−	0.0703091i	$-0.0223986\pi$
$797$	193.235	+	466.509i	0.242452	+	0.585332i	−0.755073	+	0.655641i	$0.772399\pi$
$798$		0			0
$799$	−405.227	−	882.116i	−0.507168	−	1.10402i
$800$		0			0
$801$	−232.862	+	96.4546i	−0.290714	+	0.120418i
$802$		0			0
$803$	750.109	−	750.109i	0.934133	−	0.934133i
$804$		0			0
$805$	152.618	+	767.264i	0.189588	+	0.953123i
$806$		0			0
$807$	387.123	−	934.598i	0.479707	−	1.15811i
$808$		0			0
$809$	74.2404	−	111.109i	0.0917682	−	0.137341i	−0.782745	−	0.622343i	$-0.786181\pi$
$809$	74.2404	−	111.109i	0.0917682	−	0.137341i	0.874513	+	0.485002i	$0.161181\pi$
$810$		0			0
$811$	168.725	+	252.515i	0.208046	+	0.311363i	0.920788	−	0.390064i	$-0.127547\pi$
$811$	168.725	+	252.515i	0.208046	+	0.311363i	−0.712742	+	0.701426i	$0.752547\pi$
$812$		0			0
$813$	−1049.22	−	208.702i	−1.29055	−	0.256707i
$814$		0			0
$815$			1374.47i			1.68647i
$816$		0			0
$817$	−632.617			−0.774317
$818$		0			0
$819$	−24.3282	+	122.306i	−0.0297048	+	0.149336i
$820$		0			0
$821$	−275.601	+	184.151i	−0.335689	+	0.224300i	−0.711978	−	0.702202i	$-0.752200\pi$
$821$	−275.601	+	184.151i	−0.335689	+	0.224300i	0.376288	+	0.926503i	$0.377200\pi$
$822$		0			0
$823$	−570.530	−	381.216i	−0.693232	−	0.463203i	0.158378	−	0.987379i	$-0.449373\pi$
$823$	−570.530	−	381.216i	−0.693232	−	0.463203i	−0.851610	+	0.524176i	$0.824373\pi$
$824$		0			0
$825$	22.4657	+	9.30560i	0.0272312	+	0.0112795i
$826$		0			0
$827$	1528.11	−	303.959i	1.84777	−	0.367544i	0.858402	−	0.512977i	$-0.171457\pi$
$827$	1528.11	−	303.959i	1.84777	−	0.367544i	0.989368	+	0.145432i	$0.0464574\pi$
$828$		0			0
$829$	268.158	+	268.158i	0.323471	+	0.323471i	0.850097	−	0.526626i	$-0.176543\pi$
$829$	268.158	+	268.158i	0.323471	+	0.323471i	−0.526626	+	0.850097i	$0.676543\pi$
$830$		0			0
$831$	309.226	+	746.537i	0.372113	+	0.898360i
$832$		0			0
$833$	−0.665658	−	17.5419i	−0.000799109	−	0.0210587i
$834$		0			0
$835$	−655.333	+	271.448i	−0.784830	+	0.325087i
$836$		0			0
$837$	−262.771	+	262.771i	−0.313944	+	0.313944i
$838$		0			0
$839$	148.864	+	748.392i	0.177431	+	0.892004i	0.962227	+	0.272250i	$0.0877677\pi$
$839$	148.864	+	748.392i	0.177431	+	0.892004i	−0.784796	+	0.619754i	$0.787232\pi$
$840$		0			0
$841$	301.120	−	726.968i	0.358050	−	0.864409i
$842$		0			0
$843$	−438.003	+	655.517i	−0.519576	+	0.777601i
$844$		0			0
$845$	75.8204	+	113.473i	0.0897283	+	0.134288i
$846$		0			0
$847$	−608.752	−	121.088i	−0.718716	−	0.142961i
$848$		0			0
$849$			1351.30i			1.59163i
$850$		0			0
$851$	−235.467			−0.276694
$852$		0			0
$853$	215.805	−	1084.93i	0.252996	−	1.27190i	−0.620168	−	0.784469i	$-0.712936\pi$
$853$	215.805	−	1084.93i	0.252996	−	1.27190i	0.873164	−	0.487427i	$-0.162064\pi$
$854$		0			0
$855$	130.491	−	87.1915i	0.152621	−	0.101978i
$856$		0			0
$857$	−248.011	−	165.716i	−0.289394	−	0.193367i	0.402396	−	0.915466i	$-0.368178\pi$
$857$	−248.011	−	165.716i	−0.289394	−	0.193367i	−0.691790	+	0.722099i	$0.743178\pi$
$858$		0			0
$859$	233.173	+	96.5834i	0.271447	+	0.112437i	0.514255	−	0.857637i	$-0.328068\pi$
$859$	233.173	+	96.5834i	0.271447	+	0.112437i	−0.242808	+	0.970074i	$0.578068\pi$
$860$		0			0
$861$	1346.83	−	267.901i	1.56426	−	0.311151i
$862$		0			0
$863$	853.021	+	853.021i	0.988437	+	0.988437i	0.999934	−	0.0114967i	$-0.00365959\pi$
$863$	853.021	+	853.021i	0.988437	+	0.988437i	−0.0114967	+	0.999934i	$0.503660\pi$
$864$		0			0
$865$	−233.420	−	563.526i	−0.269850	−	0.651475i
$866$		0			0
$867$	−622.262	+	487.850i	−0.717718	+	0.562688i
$868$		0			0
$869$	1309.56	−	542.437i	1.50697	−	0.624208i
$870$		0			0
$871$	−490.707	+	490.707i	−0.563383	+	0.563383i
$872$		0			0
$873$	−36.8566	−	185.291i	−0.0422183	−	0.212246i
$874$		0			0
$875$	−335.234	+	809.326i	−0.383124	+	0.924943i
$876$		0			0
$877$	441.077	−	660.118i	0.502938	−	0.752700i	−0.489950	−	0.871750i	$-0.662985\pi$
$877$	441.077	−	660.118i	0.502938	−	0.752700i	0.992888	+	0.119051i	$0.0379851\pi$
$878$		0			0
$879$	−545.722	−	816.730i	−0.620844	−	0.929158i
$880$		0			0
$881$	278.655	+	55.4279i	0.316294	+	0.0629147i	0.350684	−	0.936494i	$-0.385949\pi$
$881$	278.655	+	55.4279i	0.316294	+	0.0629147i	−0.0343906	+	0.999408i	$0.510949\pi$
$882$		0			0
$883$			101.831i			0.115324i	0.998336	+	0.0576622i	$0.0183646\pi$
$883$			101.831i			0.115324i	−0.998336	+	0.0576622i	$0.981635\pi$
$884$		0			0
$885$	99.3509			0.112261
$886$		0			0
$887$	130.325	−	655.187i	0.146928	−	0.738655i	−0.835127	−	0.550057i	$-0.814606\pi$
$887$	130.325	−	655.187i	0.146928	−	0.738655i	0.982054	−	0.188598i	$-0.0603942\pi$
$888$		0			0
$889$	−170.947	+	114.223i	−0.192291	+	0.128485i
$890$		0			0
$891$	785.279	+	524.706i	0.881345	+	0.588896i
$892$		0			0
$893$	1107.10	+	458.578i	1.23976	+	0.513525i
$894$		0			0
$895$	−297.240	+	59.1247i	−0.332111	+	0.0660611i
$896$		0			0
$897$	526.118	+	526.118i	0.586531	+	0.586531i
$898$		0			0
$899$	−36.3727	−	87.8115i	−0.0404591	−	0.0976769i
$900$		0			0
$901$	1007.42	−	38.2284i	1.11812	−	0.0424288i
$902$		0			0
$903$	527.745	−	218.599i	0.584435	−	0.242081i
$904$		0			0
$905$	463.155	−	463.155i	0.511773	−	0.511773i
$906$		0			0
$907$	−11.9096	−	59.8736i	−0.0131308	−	0.0660128i	0.973664	−	0.227986i	$-0.0732141\pi$
$907$	−11.9096	−	59.8736i	−0.0131308	−	0.0660128i	−0.986795	+	0.161973i	$0.948214\pi$
$908$		0			0
$909$	47.9840	−	115.844i	0.0527877	−	0.127441i
$910$		0			0
$911$	372.704	−	557.790i	0.409115	−	0.612284i	−0.568501	−	0.822683i	$-0.692476\pi$
$911$	372.704	−	557.790i	0.409115	−	0.612284i	0.977616	+	0.210399i	$0.0674763\pi$
$912$		0			0
$913$	−653.386	−	977.861i	−0.715647	−	1.07104i
$914$		0			0
$915$	1074.83	+	213.797i	1.17468	+	0.233658i
$916$		0			0
$917$		−	835.069i		−	0.910654i
$918$		0			0
$919$	−1500.16			−1.63238			−0.816189	−	0.577785i	$-0.803917\pi$
$919$	−1500.16			−1.63238			−0.816189	+	0.577785i	$0.803917\pi$
$920$		0			0
$921$	−168.844	+	848.836i	−0.183327	+	0.921646i
$922$		0			0
$923$	−111.774	+	74.6848i	−0.121098	+	0.0809153i
$924$		0			0
$925$	−5.24211	−	3.50267i	−0.00566715	−	0.00378667i
$926$		0			0
$927$	224.216	+	92.8731i	0.241872	+	0.100187i
$928$		0			0
$929$	1472.06	−	292.811i	1.58456	−	0.315189i	0.677285	−	0.735721i	$-0.263156\pi$
$929$	1472.06	−	292.811i	1.58456	−	0.315189i	0.907278	+	0.420532i	$0.138156\pi$
$930$		0			0
$931$	15.3230	+	15.3230i	0.0164587	+	0.0164587i
$932$		0			0
$933$	−54.1320	−	130.686i	−0.0580193	−	0.140071i
$934$		0			0
$935$	1107.14	−	508.600i	1.18411	−	0.543957i
$936$		0			0
$937$	285.073	−	118.081i	0.304240	−	0.126020i	−0.225340	−	0.974280i	$-0.572349\pi$
$937$	285.073	−	118.081i	0.304240	−	0.126020i	0.529580	+	0.848260i	$0.322349\pi$
$938$		0			0
$939$	354.402	−	354.402i	0.377425	−	0.377425i
$940$		0			0
$941$	−102.404	−	514.821i	−0.108825	−	0.547100i	−0.996278	−	0.0862011i	$-0.972527\pi$
$941$	−102.404	−	514.821i	−0.108825	−	0.547100i	0.887453	−	0.460898i	$-0.152473\pi$
$942$		0			0
$943$	−634.315	+	1531.37i	−0.672656	+	1.62394i
$944$		0			0
$945$	−546.630	+	818.090i	−0.578445	+	0.865704i
$946$		0			0
$947$	353.521	+	529.081i	0.373306	+	0.558691i	0.969792	−	0.243931i	$-0.0784372\pi$
$947$	353.521	+	529.081i	0.373306	+	0.558691i	−0.596487	+	0.802623i	$0.703437\pi$
$948$		0			0
$949$	852.386	+	169.550i	0.898194	+	0.178662i
$950$		0			0
$951$		−	565.118i		−	0.594236i
$952$		0			0
$953$	−188.797			−0.198109			−0.0990543	−	0.995082i	$-0.531582\pi$
$953$	−188.797			−0.198109			−0.0990543	+	0.995082i	$0.531582\pi$
$954$		0			0
$955$	81.6541	−	410.503i	0.0855016	−	0.429846i
$956$		0			0
$957$	−242.912	+	162.308i	−0.253826	+	0.169601i
$958$		0			0
$959$	−1147.54	−	766.762i	−1.19660	−	0.799543i
$960$		0			0
$961$	−733.676	−	303.898i	−0.763450	−	0.316231i
$962$		0			0
$963$	105.884	−	21.0617i	0.109952	−	0.0218709i
$964$		0			0
$965$	908.806	+	908.806i	0.941768	+	0.941768i
$966$		0			0
$967$	398.534	+	962.147i	0.412135	+	0.994982i	0.984564	+	0.175027i	$0.0560013\pi$
$967$	398.534	+	962.147i	0.412135	+	0.994982i	−0.572429	+	0.819955i	$0.693999\pi$
$968$		0			0
$969$	153.985	−	963.850i	0.158911	−	0.994686i
$970$		0			0
$971$	−1192.78	+	494.065i	−1.22840	+	0.508821i	−0.900072	−	0.435742i	$-0.856486\pi$
$971$	−1192.78	+	494.065i	−1.22840	+	0.508821i	−0.328331	+	0.944563i	$0.606486\pi$
$972$		0			0
$973$	1163.38	−	1163.38i	1.19566	−	1.19566i
$974$		0			0
$975$	3.88655	+	19.5390i	0.00398620	+	0.0200400i
$976$		0			0
$977$	14.6247	−	35.3071i	0.0149690	−	0.0361383i	−0.916218	−	0.400679i	$-0.868774\pi$
$977$	14.6247	−	35.3071i	0.0149690	−	0.0361383i	0.931187	+	0.364541i	$0.118774\pi$
$978$		0			0
$979$	1341.96	−	2008.38i	1.37074	−	2.05146i
$980$		0			0
$981$	−82.7564	−	123.854i	−0.0843592	−	0.126252i
$982$		0			0
$983$	−540.707	−	107.553i	−0.550058	−	0.109413i	−0.0877661	−	0.996141i	$-0.527973\pi$
$983$	−540.707	−	107.553i	−0.550058	−	0.109413i	−0.462292	+	0.886728i	$0.652973\pi$
$984$		0			0
$985$			784.391i			0.796336i
$986$		0			0
$987$	−1082.04			−1.09629
$988$		0			0
$989$	−134.515	+	676.252i	−0.136011	+	0.683774i
$990$		0			0
$991$	−16.3189	+	10.9040i	−0.0164671	+	0.0110030i	−0.563777	−	0.825927i	$-0.690652\pi$
$991$	−16.3189	+	10.9040i	−0.0164671	+	0.0110030i	0.547309	+	0.836930i	$0.315652\pi$
$992$		0			0
$993$	551.293	+	368.362i	0.555179	+	0.370959i
$994$		0			0
$995$	−588.631	−	243.819i	−0.591589	−	0.245044i
$996$		0			0
$997$	−416.673	+	82.8814i	−0.417927	+	0.0831308i	−0.399574	−	0.916701i	$-0.630842\pi$
$997$	−416.673	+	82.8814i	−0.417927	+	0.0831308i	−0.0183524	+	0.999832i	$0.505842\pi$
$998$		0			0
$999$	−209.411	−	209.411i	−0.209620	−	0.209620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.65.2	✓	32
4.3	odd	2		272.3.bh.f.65.3		32
17.11	odd	16	inner	136.3.t.a.113.2	yes	32
68.11	even	16		272.3.bh.f.113.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.65.2	✓	32	1.1	even	1	trivial
136.3.t.a.113.2	yes	32	17.11	odd	16	inner
272.3.bh.f.65.3		32	4.3	odd	2
272.3.bh.f.113.3		32	68.11	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.533765 + 2.68342i) q^{3} +(-4.10611 + 2.74362i) q^{5} +(-5.75863 - 3.84780i) q^{7} +(1.39909 + 0.579524i) q^{9} +O(q^{10})\)	\(q+(-0.533765 + 2.68342i) q^{3} +(-4.10611 + 2.74362i) q^{5} +(-5.75863 - 3.84780i) q^{7} +(1.39909 + 0.579524i) q^{9} +(-14.2338 + 2.83128i) q^{11} +(-8.40728 - 8.40728i) q^{13} +(-5.17057 - 12.4829i) q^{15} +(15.9413 + 5.90538i) q^{17} +(-19.3881 + 8.03080i) q^{19} +(13.3990 - 13.3990i) q^{21} +(4.46220 + 22.4330i) q^{23} +(-0.234360 + 0.565794i) q^{25} +(-15.9822 + 23.9190i) q^{27} +(-4.08770 - 6.11768i) q^{29} +(12.6698 + 2.52018i) q^{31} -39.7065i q^{33} +34.2025 q^{35} +(-2.00841 + 10.0970i) q^{37} +(27.0478 - 18.0727i) q^{39} +(60.2557 + 40.2616i) q^{41} +(27.8507 + 11.5362i) q^{43} +(-7.33483 + 1.45899i) q^{45} +(-40.3775 - 40.3775i) q^{47} +(-0.395167 - 0.954017i) q^{49} +(-24.3555 + 39.6252i) q^{51} +(54.7887 - 22.6942i) q^{53} +(50.6777 - 50.6777i) q^{55} +(-11.2013 - 56.3128i) q^{57} +(-2.81393 + 6.79342i) q^{59} +(-45.0615 + 67.4393i) q^{61} +(-5.82698 - 8.72069i) q^{63} +(57.5876 + 11.4549i) q^{65} -58.3669i q^{67} -62.5788 q^{69} +(2.20576 - 11.0891i) q^{71} +(-60.7769 + 40.6098i) q^{73} +(-1.39317 - 0.930886i) q^{75} +(92.8615 + 38.4645i) q^{77} +(-95.7936 + 19.0545i) q^{79} +(-46.0167 - 46.0167i) q^{81} +(31.0115 + 74.8684i) q^{83} +(-81.6590 + 19.4888i) q^{85} +(18.5982 - 7.70361i) q^{87} +(-117.689 + 117.689i) q^{89} +(16.0649 + 80.7640i) q^{91} +(-13.5254 + 32.6532i) q^{93} +(57.5761 - 86.1688i) q^{95} +(-69.3086 - 103.728i) q^{97} +(-21.5552 - 4.28760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

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Database

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